I will say to you what I say to my son about playing games.....you need to spec your character to how you play... What this means is what works for you may not be the best for me and vice versa.
I don't know if my way is even the best for me, as I will tweak and try stuff but currently this is my thoughts on what you chose as it seems to me and how I play and what you describe as your playstyle.
1) Shotgun: Rank 4 Spare ammo?? Why, if you are running Scattershot which has infinite ammo then this is wasted and usually ammo shouldn't be an issue for an adept anyway, so I would always choose Weight instead to lessen chance of effecting cooldowns. Otherwise 5 and 6th level are good.
2) Combat Fitness: Rank 5 heavy lifting wouldn't be my choice, instead I would have gone with Extra holster and thus more options on weight and weapons carried....but using Scattershot with extra 20% clip is good enough to not be a bad choice just a different one than I would use in my play. 4 and 6th options are good.
3) Combat Tools: You said you were playing mostly from cover so this is mostly a wasted skillset for you especially early when points are important. The only thing you get from this group is better melee and cutting damage in half when dodging(you say you play from cover...) and better aerial damage/DR... Personally I would only start really taking this after I had most other things up where I wanted unless I was running a more active character, such as when you see me running Annihailation and really getting up in people's face.
4) Pull: To me level 5 crushing grip is less ideal than Expose. I am not usually holding onto enemies for a long time, they are usually flying through the air at something, exploding or being tossed off the map, and thus the 30% defense debuff is WAY WAY more effective than 35pts of damage per second. Since the debuff is all all incoming damage, while effected, any impacts, bullets or explosions hurt them worse, so yeah, debuff is king to me. 4th and 6th are fine to me.
5) Throw: I personally don't see the advantage of area throw unless you are trying to bowl groups over. I take damage and force, which usually isn't a big priority for me as an adept, as I am playing more exploder BUT in this case I like to add extra hit when I pull throw an enemy when they run into a wall....add this to debuff from pull and they hurt.... 5th and 6th are fine.
6) Singularity: Here is a playstyle difference. I don't really like expanding singularity......my playstyle doesn't suit it much. I use Singularity as a primer, but I also use it as a grenade to strip defenses and knock things out of cover. Since I often play a very mobile Adept I don't leave it planted somewhere and drag things to it, so I agree with Radius at 4th, but I chose Anti-shield which is supposed to increase damage against shields, and also Exploding Singularity which does damage when Singularity ends either after it's entire duration or when you tap the power again and detonate it at your choice of time. When you detonate it early, the cooldown is reduced and while I haven't checked the numbers to be sure, it seems to me that the bonus to damage on shields SHOULD also be boosted due to level 5 Anti-Shield....again, haven't actually checked it to make 100% sure.
7) Barrier: All good choices you made to me.
8) Offensive Biotics: Your choices are all good to me.
9) Containment: 4th and 6th good, I would disagree with you on rank 5. Knocking people down is good, especially if you are moving around and don't want them shooting at you, but to my mind, the 50% bonus to shields is better as it is often hard to see/find enemies who are laying on the ground and they often can't be effected by biotics when in the getting up animations. I like the extra damage to shields as usually shields in this game means higher difficulty enemies who are likely to do WAY more damage to me than the average enemy. So I want things to strip those shields fast, so I am able to float them or otherwise hinder their ability to kill me.
10) Team Support: Here is a playstyle difference of opinion....Rank 4 I choose support as I am often running Cora who boosts shields and health with here shield boost power so I want this maxed. I also don't really need huge damage output from my team, just enough to occupy enemies so they don't all concentrate on me, so boosting their damage isn't a huge priority. Also most times they seem to do well and have more shields than me, so having improved recovery isn't high on my list....most times my teammates die on bosses or some huge battle, not in a skirmish which will be over shortly. If they die in a skirmish, it isn't a big deal, they will pop up in 30 second or so anyway when it is over, and if they die from fighting a boss then I want the highest DR I can to revive them as because no amount of boosted shield recovery will help them when facing a boss battle. So I choose Tactical Revive at level 5 to go along with Support for level 4 and I agree with Defense Grid at level 6.
Loadout:
Looks good, I personally don't like the Asari Sword, preferring the Cryo Gauntlet, even though it does less damage, sometimes the freeze is helpful and usually melee isn't high on my list of having to max. I use it and it is fun, but it is more a finisher and not a goto damage move, and my personal dislike of the animation for the Asari Sword is enough to make me not use it. I usually run a few bonus to Combo Radiuses instead of full Combo damage bonuses, but having that much bonus to damage isn't bad, just a playstyle difference of opinion. The mod of Rapid Deployment is a good choice. The Shotgun is ok early, but usually I prefer a rapid fire pistol with ether sniper or another heavy pistol combo instead of the Shotgun. I pick up the Shotgun usually later, when I am usually mixing it up with annihilation and need to quick burst damage up close. But again this is playstyle difference.
Mechanics:
Sounds like a solid build and playstyle, but you may want to consider some changes if you don't really like playing this way. Substitute Annihilation for Singularity add Lance and run the Asari Adept build from MP. Try the exploding Singularity and use pull as main primer and try to create a more mobile Adept for most occasions. The higher level you get, the faster you can make your powers regin so you can become extremely fast in casting allowing greater movement and activity when fighting.
One thing to consider for later levels of the game....for every point put into combat you get more health for your character, and your weapons do more damage, plus for every point in Tech you get more shields...So even if you are playing an Adept putting points after you have maxed out Biotics into Tech and combat isn't wasting points but instead buffing your character.